The relative Langlands program via gauge theory

          @misc{ scivideos_PIRSA:22060091,
            doi = {10.48660/22060091},
            url = {https://pirsa.org/22060091},
            author = {Ben-Zvi, David},
            keywords = {Mathematical physics},
            language = {en},
            title = {The relative Langlands program via gauge theory},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060091 see, \url{https://scivideos.org/pirsa/22060091}}
          }
          

Abstract

I will discuss a close parallel between Gaiotto and Witten's S-duality for supersymmetric boundary conditions in 4d N=4 SYM and the relative Langlands program, an enhancement of the Langlands program that was developed to provide a framework for the theory of integral representations of L-functions. A special and conjecturally self-dual class of boundary conditions is provided by quantizations of "small" or "multiplicity-free" hamiltonian spaces called hyperspherical varieties. I'll explain how a hyperspherical variety produces objects of interest in all the different settings of the Langlands program (local / global, geometric / arithmetic) and a collection of conjectures providing S-dual descriptions of these objects. The talk is based on forthcoming joint work with Yiannis Sakellaridis and Akshay Venkatesh.